For example,
consider the functor categories \({\operatorname{FinSets}}^{\mathcal {D}}\) 
for a finite category \({\mathcal {D}}\) .
It is locally finite, and is shown to be
combinatorial, by methods in for example [1]} [2]}.
It is an elementary topos, and hence is extensive [3]},
and has finite products.
By Theorems REF , REF  and Corollary REF ,
\({{\operatorname{Dec}}}({\operatorname{FinSets}}^{\mathcal {D}},+,-,\times )\)  embeds into a direct product of
copies of \({\mathbb {Z}}\) . In particular, there are no nilpotent elements.
By the same argument, a similar embedding is obtained for the category of
\(G\) -finite sets where \(G\)  is a group, which is known as a theorem
by Burnside.
